Dr. Casey Doyle defended his Ph.D. thesis in Physics entitles Introducing Non-Markovian and Empirical Effects into Social Interaction Models supervised jointly by Gyorgy Korniss and Boleslaw K. Szymanski. The excerpt from the abstract is provided here. The thesis focuses on stochastic models of opinion spread used for simulating and predicting the social behaviors of large populations. Yet, some assumptions made in these base models differ from the natural behavioral patterns of real people. The thesis presents two such model extensions, building off of the basic examples of the naming game and voter models to create more in depth systems and describe complex phenomenon.
The first of the two models presents a system in which opinions maintain certain inertia to changing it so a node holding that opinion will resist switching opinions. The second model extension replaces the speaker selection mechanic to allow for non-exponential distributions of waiting time to speak that vary the activity patterns of the nodes. In both of these scenarios it is shown that the symmetry of the system is broken, creating well defined tipping points where the advantaged opinion is able to build a consensus quickly and consistently. Further, despite both extensions breaking the Markov property maintained in the more basic models, analytic approximations that accurately describe the behavior of the systems are provided. Finally, a brief overview of relevant empirical investigations is provided to inform on future work in this area. First, data mining techniques are employed to find frequent response patterns in a large survey data set on opinion formation with regards to media consumption. These results serve to identify both groups of individuals that behave similarly and the general trends that shape their responses. Then, a large scale cell phone data set is analyzed for its capability to provide an empirical social network. Two separate network building schemes are compared and used to provide effective networks that may serve as the setting for future simulations.